How to find number of strings generated by permuting the given string satisfying the below conditions?

The question goes like this-

How many strings can be generated by permuting the characters of “abbbbcccdeff” such that there are only 3 mismatchings and the rest 9 are same ?

My attempt-

Obviously, If the string was having only distinct characters(like-“abcdefghijkl“) then the answer would have been- 2*(12C9)=440 strings[as there are 12 characters and 9 of them have to be same]. I can calculate this for strings having distinct characters only, but I am failing to generalise this for strings with repeating characters.

I can manually find all pairs,but this method is very time-consuming,like-for the case of- “abbbcc” there comes a total of 12 such strings . These are-
bbbcac,bbbcca,bbcbac,bbcbca,bcbbac,bcbbca,cabbbc,cabbcb,cbabbc,cbabcb,cbbabc,cbbacb

Where I am failing?

I need a quick solution(some kind of generalised formula) instead of counting it manually

Solutions Collecting From Web of "How to find number of strings generated by permuting the given string satisfying the below conditions?"

There is $1$ letter with $4$ occurrences, $1$ letter with $3$ occurrences, $1$ letter with $2$ occurrences and $3$ letters with $1$ occurrence. Thus the number of triples of distinct letters is

$$
\binom30(4\cdot3\cdot2)+\binom31(4\cdot3\cdot1)+\binom31(4\cdot2\cdot1)+\binom31(3\cdot2\cdot1)+\binom32(4+3+2)\cdot1+\binom33=24+36+24+18+27+1=130\;.
$$

Each of these can be permuted in $2$ ways, for a total of $2\cdot130=260$ permutations.